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Finding A Function From A Power Series

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the sum of the series and its radius of convergence:

    [itex]\sum_{n=1}^{\infty} (-1)^{n+1}\frac{(x-1)^n}{n}[/itex]


    2. Relevant equations



    3. The attempt at a solution
    I found the radius of convergence, but I wasn't sure how to find the sum of the power series.
     
  2. jcsd
  3. Oct 29, 2012 #2

    LCKurtz

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    Hint: If you call that series f(x), what is f'(x)?
     
  4. Oct 29, 2012 #3
    Would it be [itex]f'(x) = \sum_{n=0}^{\infty} (-1)^{n+1}(x-1)^{n-1}[/itex]?
     
  5. Oct 29, 2012 #4

    LCKurtz

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    Yes. And do you recognize what kind of series that is?
     
  6. Oct 29, 2012 #5
    If you distribute the (-1)^(n+1) to the (x-1)^(n-1) would it be a geometric series?
     
  7. Oct 29, 2012 #6

    LCKurtz

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    Do you really have to ask? What do you think? Why? Show us what you would do if it is.
     
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